ZETETIC ASTRONOMY.

The term “zetetic” is derived from the Greek verbzeteo; which means to search or examine—to proceed only by inquiry. None can doubt that by making special experiments and collecting manifest and undeniable facts, arranging them in logical order, and observing what is naturally and fairly deducible, the result will be far more consistent and satisfactory than by framing a theory or system and assuming the existence of causes for which there is no direct evidence, and which can only be admitted “for the sake of argument.” All theories are of this character—“supposing instead of inquiring, imagining systems instead of learning from observation and experience the true constitution of things. Speculative men, by the force of genius may invent systems that will perhaps be greatly admired for a time; these, however, are phantoms which the force of truth will sooner or later dispel; and while we are pleased with the deceit, true philosophy, with all the arts and improvements that depend upon it, suffers. The real state of things escapes our observation; or, if it presents itself to us, we are apt either to reject itwholly as fiction, or, by new efforts of a vain ingenuity to interweave it with our own conceits, and labour to make it tally with our favourite schemes. Thus, by blending together parts so ill-suited, the whole comes forth an absurd composition of truth and error. * * These have not done near so much harm as that pride and ambition which has led philosophers to think it beneath them to offer anything less to the world than a complete and finished system of nature; and, in order to obtain this at once, to take the liberty of inventing certain principles and hypotheses, from which they pretend to explain all her mysteries.”[1]

[1]“An Account of Sir Isaac Newton’s Discoveries.” By Professor Maclaurin, M.A., F.R.S., of the Chair of Mathematics in the University of Edinburgh.

Copernicus admitted, “It is not necessary that hypotheses should be true, or even probable; it is sufficient that they lead to results of calculation which agree with calculations. * * Neither let any one, so far as hypotheses are concerned, expect anythingcertainfrom astronomy; since that science can afford nothing of the kind; lest, in case he should adopt for truth things feigned for another purpose, he should leave this study more foolish than he came. * * The hypothesis of the terrestrial motion wasnothing but an hypothesis, valuable only so far as it explained phenomena, and not considered with reference to absolute truth or falsehood.” TheNewtonian and all other “systems of nature” are little better than the “hypothesis of the terrestrial motion” of Copernicus. The foundations or premises are always unproved; no proof is ever attempted; the necessity for it is denied; it is considered sufficient that the assumptions shallseemto explain the phenomena selected. In this way it is that one theory supplants another; that system gives way to system as one failure after another compels opinions to change. This will ever be so; there will always exist in the mind a degree of uncertainty; a disposition to look upon philosophy as a vain pretension; a something almost antagonistic to the highest aspirations in which humanity can indulge, unless the practice of theorising be given up, and the method of simple inquiry, the “zetetic” process be adopted. “Nature speaks to us in a peculiar language; in the language of phenomena, she answers at all times the questions which are put to her; and such questions are experiments.”[2]Not experiments only which corroborate what has previously beenassumedto be true; but experiments in every form bearing on the subject of inquiry, before a conclusion is drawn or premises affirmed.

[2]“Liebig’s Agricultural Chemistry,” p. 39.

We have an excellent example of zetetic reasoning in an arithmetical operation; moreespecially so in what is called the “Golden Rule,” or the “Rule-of-Three.” If one hundred weight of any article is worth a given sum, what will some other weight of that article be worth? The separate figures may be considered as the elements or facts of the inquiry; the placing and working of these as the logical arrangement; and the quotient or answer as the fair and natural deduction. Hence, in every zetetic process, the conclusion arrived at is essentially a quotient, which, if the details be correct, must, of necessity, be true beyond the reach or power of contradiction.

In our courts of Justice we have also an example of the zetetic process. A prisoner is placed at the bar; evidence for and against him is advanced; it is carefully arranged and patiently considered; and only such a verdict given as could not in justice be avoided. Society would not tolerate any other procedure; it would brand with infamy whoever should assume a prisoner to be guilty, and prohibit all evidence but such as would corroborate the assumption. Yet such is the character of theoretical philosophy!

The zetetic process is also the natural method of investigation; nature herself teaches it. Children invariably seek information by asking questions—by earnestly inquiring from thosearound them. Question after question in rapid and exciting succession will often proceed from a child, until the most profound in learning and philosophy will feel puzzled to reply. If then both nature and justice, as well as the common sense and practical experience of mankind demand, and will not be content with less or other than the zetetic process, why should it be ignored and violated by the learned in philosophy? Let the practice of theorising be cast aside as one fatal to the full development of truth; oppressive to the reasoning power; and in every sense inimical to the progress and permanent improvement of the human race.

If then we adopt the zetetic process to ascertain the true figure and condition of the Earth, we shall find that instead of its being a globe, and moving in space, it is the directly contrary—A Plane; without motion, and unaccompanied by anything in the Firmament analogous to itself.

If the Earth is a globe, and 25,000 miles in circumference, the surface of all standing water must have a certain degree of convexity—every part must be an arc of a circle, curvating from the summit at the rate of 8 inches per mile multiplied by the square of the distance. That this may be sufficiently understood, the following quotation is given from theEncyclopædiaBritannica, art. “Levelling.” “If a line which crosses the plumb-line at right angles be continued for any considerable length it will rise above the Earth’s surface (the Earth being globular); and this rising will be as the square of the distance to which the said right line is produced; that is to say, it is raised eight inches very nearly above the Earth’s surface at one mile’s distance; four times as much, or 32 inches, at the distance of two miles; nine times as much, or 72 inches, at the distance of three miles. This is owing to the globular figure of the Earth, and this rising is the difference between the true and apparent levels; the curve of the Earth being the true level, and the tangent to it the apparent level. So soon does the difference between the true and apparent levels become perceptible that it is necessary to make an allowance for it if the distance betwixt the two stations exceeds two chains.

FIG. 1.

Let B. D. be a small portion of the Earth’s circumference, whose centre of curvature is A. and consequently all the points of this arc will be on a level. But a tangent B. C. meeting the vertical line A. D. in C. will be the apparentlevel at the point B. and therefore D. C. is the difference between the apparent and the true level at the point B.

The distance C. D. must be deducted from the observed height to have the true difference of level; or the differences between the distances of two points from the surface of the Earth or from the centre of curvature A. But we shall afterwards see how this correction may be avoided altogether in certain cases. To find an expression for C. D. we have Euclid, third book, 36 prop. which proves that B. C² = C. D. (2A D×C D); but since in all cases of levelling C. D. is exceedingly small compared with 2 A. D., we may safely neglect C. D² and then B C² = 2 A. D × C. D. or C. D =B. C²2 A. D. Hence the depression of the true level is equal to the square of the distance divided by twice the radius of the curvature of the Earth.

For example, taking a distance of four miles, the square of 4 = 16, and putting down twice the radius of the Earth’s curvature as in round figures about 8000 miles, we make the depression on four miles =168000of a mile =16 × 17608000yards =17650yards =52850feet, or rather better than 10¹⁄₂ feet.

Or, if we take the mean radius of the Earth as the mean radius of its curvature, and consequently 2 A. D = 7,912 miles, then 5,280 feet being 1 mile, we shall have C. D. the depression in inches5280 × 12 × B C²7912= 8008 B. C² inches.

The preceding remarks suppose the visual ray C. B. to be a straight line, whereas on account of the unequal densities of the air at different distances from the Earth, the rays of light are incurvated by refraction. The effect of this is to lessen the difference between the true and apparent levels, but in such an extremely variable and uncertain manner that if any constant or fixed allowance is made for it in formulæ or tables, it will often lead to a greater error than what it was intended to obviate. For though the refraction may at a mean compensate for about a seventh of the curvature of the earth, it sometimes exceeds a fifth, and at other times does not amount to a fifteenth. We have, therefore, made no allowance for refraction in the foregone formulæ.”

If the Earth is a globe, there cannot be a question that, however irregular thelandmay be in form, thewatermust have a convex surface. And as the difference between the true and apparent level, or the degree of curvature would be 8 inches in one mile, and in every succeeding mile 8 inches multiplied by the square of the distance, there can be no difficulty in detecting either its actual existence or proportion. Experiments made upon the sea have been objected to on account of its constantly-changing altitude; and the existence of banks and channels which producea “a crowding” of the waters, currents, and other irregularities. Standing water has therefore been selected, and many important experiments have been made, the most simple of which is the following:—In the county of Cambridge there is an artificial river or canal, called the “Old Bedford.” It is upwards of twenty miles long, and passes in a straight line through that part of the fens called the “Bedford level” The water is nearly stationery—often entirely so, and throughout its entire length has no interruption from locks or water-gates; so that it is in every respect well adapted for ascertaining whether any and what amount of convexity really exists. A boat with a flag standing three feet above the water, was directed to sail from a place called “Welney Bridge,” to another place called “Welche’s Dam.” These two points are six statute miles apart. The observer, with a good telescope, was seated in the water as a bather (it being the summer season), with the eye not exceeding eight inches above the surface. The flag and the boat down to the water’s edge were clearlyvisible throughout the whole distance!From this observation it was concluded that the water did not decline to any degree from the line of sight; whereas the water would be 6 feet higher in the centre of the arc of 6 miles extent than at the two places WelneyBridge and Welche’s Dam; but as the eye of the observer was only eight inches above the water, the highest point of the surface would be at one mile from the place of observation; below which point the surface of the water at the end of the remaining five miles would be 16 feet 8 inches (5² × 8 = 200 inches). This will be rendered clear by the following diagram:—

Boating experimentFIG. 2.

FIG. 2.

Let A B represent the arc of water from Welney Bridge to Welche’s Dam, six miles in length; and A L the line of sight, which is now a tangent to the arc A B; the point of contact, T, is 1 mile from the eye of the observer at A; and from T to the boat at B is 5 miles; the square of 5 miles multiplied by 8 inches is 200 inches, or, in other words, that the boat at B would have been 200 inches or above 16 feet below the surface of the water at T; and the flag on the boat, which was 3 feet high, would have been 13 feet below the line-of-sight, A T L!!

From this experiment it follows that the surface of standing water isnot convex, andthereforethat the Earthis not a Globe! On the Contrary, this simple experiment is all-sufficient to prove that the surface of the water is parallel to the line-of-sight, and is therefore horizontal, and that the Earthcannotbe other thana Plane! In diagramFigure 3this is perfectly illustrated.

Boating experimentFIG. 3.

FIG. 3.

A B is the line-of-sight, and C D the surface of the water equidistant from or parallel to it throughout the whole distance observed.

Although, on account of the variable state of the water, objections have been raised to experiments made upon the sea-shore to test the convexity of the flood or ebb-tide level, none can be urged against observations made from higher altitudes. For example,—the distance across the Irish Sea between Douglas Harbour, in the Isle of Man, and the Great Orm’s Head in North Wales is 60 miles. If the earth is a globe, the surface of the water would form an arc 60 miles in length, the centre of which would be 1,944 feet higher than the coast line at either end, so that an observer would be obliged to attain this altitude before he could see the Welshcoast from the Isle of Man: as shown in the diagram,Figure 4.

Irish SeaFIG. 4.

FIG. 4.

It is well known, however, that from an altitude not exceeding 100 feet the Great Orm’s Head is visible in clear weather from Douglas Harbour. The altitude of 100 feet could cause the line of sight to touch the horizon at the distance of nearly 13 miles; and from the horizon to Orm’s Head being 47 miles, the square of this number multiplied by 8 inches gives 1472 feet as the distance which the Welsh coast line would be below the line of sight B C.—A representing the Great Orm’s Head, which, being 600 feet high, its summit would be 872 feet below the horizon.

Many similar experiments have been made across St. George’s Channel, between points near Dublin and Holyhead, and always with results entirely incompatible with the doctrine of rotundity.

Again, it is known that the horizon at sea, whatever distance it may extend to the rightand left of the observer on land, always appears as a straight line. The following experiment has been tried in various parts of the country. At Brighton, on a rising ground near the race course, two poles were fixed in the earth six yards apart, and directly opposite the sea. Between these poles a line was tightly stretched parallel to the distant horizon. From the centre of the line the view embraced not less than 20 miles on each side, making a distance of 40 miles. A vessel was observed sailing directly westwards; the line cut the rigging a little above the bulwarks, which it did for several hours or until the vessel had sailed the whole distance of 40 miles. This will be understood by reference to the diagram,Figure 5.

Brighton experimentFIG. 5.

FIG. 5.

If the Earth were a globe, the appearance would be as represented inFigure 6.

Brighton experimentFIG. 6.

FIG. 6.

Brighton experimentFIG. 7.

FIG. 7.

The ship coming into view from the east would have to ascend an inclined plane for 20 miles until it arrived at the centre of the arc A B, whence it would have to descend for the same distance. The square of 20 miles multiplied by 8 inches gives 266 feet as the amount the vessel would be below the line C D at the beginning and at the end of the 40 miles.

If we stand upon the deck of a ship, or mount to the mast head; or go to the top of a mountain, or ascend above the Earth in a balloon, and look over the sea, the surface appears as a vast inclined plane rising up until in the distance it intercepts the line of sight. If a good mirror be held in the opposite direction, the horizon will be reflected as a well-defined mark or line across the centre, as represented in diagram,Figure 7.

Ascending or descending, the distant horizon does the same. It rises and falls with theobserver, and is always on a level with his eye. If he takes a position where the water surrounds him—as at the mast-head of a ship out of sight of land, or on the summit of a small island far from the mainland, the surface of the sea appears to rise up on all sides equally and to surround him like the walls of an immense amphitheatre. He seems to be in the centre of a large concavity, the edges of which expand or contract as he takes a higher or lower position. This appearance is so well known to sea-going travellers that nothing more need be said in its support. But the appearance from a balloon is familiar only to a small number of observers, and therefore it will be useful to quote from those who have written upon the subject.

“The Apparent Concavity of the Earth as seen from a Balloon.—A perfectly-formed circle encompassed the visible planisphere beneath, or rather the concavo-sphere it might now be called, for I had attained a height from which the surface of the Earth assumed a regularly hollowed or concave appearance—an optical illusion which increases as you recede from it. At the greatest elevation I attained, which was about a mile-and-a-half, the appearance of the World around me assumed a shape or form like that which is made by placing two watch-glasses together by their edges, the balloon apparently in the central cavity all the time of its flight at that elevation.”—Wise’s Aeronautics.“Another curious effect of the aerial ascent was, that the Earth, when we were at our greatest altitude, positively appearedconcave, looking like a huge dark bowl, rather thanthe convex sphere such as we naturally expect to see it. * * * The horizon always appears to be on a level with our eye, and seems to rise as we rise, until at length the elevation of the circular boundary line of the sight becomes so marked that the Earth assumes the anomalous appearance as we have said of aconcaverather than aconvexbody.”—Mayhew’s Great World of London.

“Another curious effect of the aerial ascent was, that the Earth, when we were at our greatest altitude, positively appearedconcave, looking like a huge dark bowl, rather thanthe convex sphere such as we naturally expect to see it. * * * The horizon always appears to be on a level with our eye, and seems to rise as we rise, until at length the elevation of the circular boundary line of the sight becomes so marked that the Earth assumes the anomalous appearance as we have said of aconcaverather than aconvexbody.”—Mayhew’s Great World of London.

Mr. Elliott, an American æronaut, in a letter giving an account of his ascension from Baltimore, thus speaks of the appearance of the Earth from a balloon:—

“I don’t know that I ever hinted heretofore that the æronaut may well be the most sceptical man about the rotundity of the Earth. Philosophy imposes the truth upon us; but the view of the Earth from the elevation of a balloon is that of an immense terrestrial basin, the deeper part of which is that directly under one’s feet. As we ascend, the Earth beneath us seems to recede—actually to sink away—while the horizon gradually and gracefully lifts a diversified slope stretching away farther and farther to a line that, at the highest elevation, seems to close with the sky. Thus upon a clear day, the æronaut feels as if suspended at about an equal distance between the vast blue oceanic concave above, and the equally expanded terrestrial basin below.”“The chief peculiarity of the view from a balloon, at a considerable elevation, was the altitude of the horizon, which remained practically on a level with the eye at an elevation of two miles, causing the surface of the Earth to appearconcaveinstead ofconvex, and to recede during the rapid ascent, whilst the horizon and the balloon seemed to be stationary.”—London Journal, July 18, 1857.

“The chief peculiarity of the view from a balloon, at a considerable elevation, was the altitude of the horizon, which remained practically on a level with the eye at an elevation of two miles, causing the surface of the Earth to appearconcaveinstead ofconvex, and to recede during the rapid ascent, whilst the horizon and the balloon seemed to be stationary.”—London Journal, July 18, 1857.

During the important balloon ascents recently made for scientific purposes by Mr. Coxwell andMr. Glaisher, of the Royal Greenwich Observatory, the same phenomenon was observed—

“The horizon always appeared on a level with the car.”—Vide “Glaisher’s Report.”

The following diagram represents this appearance:—

BalloonFIG. 8.

FIG. 8.

The surface of the earth C D appears to rise to the line-of-sight from the balloon, and “seems to close with the sky” at the points H H in the same manner that the ceiling and the floor of a long room, or the top and bottom of a tunnel appear to approach each other, and from the same cause, viz.: that they areparallel to the line-of-sight, and therefore horizontal.

If the Earth’s surface were convex the observer, looking from a balloon, instead of seeing it gradually ascend to the level of the eye, wouldhave to look downwards to the horizon H H, as represented infigure 9, and the amount of dip in the line-of-sight C H would be the greatest at the highest elevation.

Balloon flightFIG. 9.

FIG. 9.

Many more experiments have been made than are here described, but the selection now given is amply sufficient to prove that the surface of water is horizontal, and that the Earth, taken as a whole, its land and water together, is not a globe, has really no degree of sphericity; but is “to all intents and purposes”A PLANE!

If we now consider the fact that when we travel by land or sea, and from any part of the known world, in a direction towards the North polar star, we shall arrive at one and the same point, we are forced to the conclusion that what has hitherto been called the North Polar region, is reallythe Centre of the Earth. Thatfrom this northern centre the land diverges and stretches out, of necessity, towards a circumference, which must now be calledthe Southern Region: which is a vast circle, and not a pole or centre. That there isOne Centre—the North, andOne Circumference—the South. This language will be better understood by reference to the diagramFigure 10.

Map of flat earthFIG. 10.

FIG. 10.

N represents the northern centre; and S S S the southern circumference—both icy or frozenregions. That the south is an immense ring, or glacial boundary, is evident from the fact, that within the antarctic circle the most experienced, scientific, and daring navigators have failed in their attempts to sail, in a direct manner, completely round it. Lieut. Wilkes, of the American Navy, after great and prolonged efforts, and much confusion in his reckoning, and seeing no prospect of success, was obliged to give up his attempt and return to the north. This he acknowledged in a letter to Captain Sir James Clarke Ross, with whose intention to explore the south seas he had become acquainted, in which the following words occur: “I hope you intend to circumnavigate the antarctic circle. I made 70 degrees of it.” Captain Ross, however, was himself greatly confused in his attempts to navigate the southern region. In his account of the voyage he says, at page 96—“We found ourselves every day from 12 to 16 miles by observation in advance of our reckoning.” “By our observations we found ourselves 58 miles to the eastward of our reckoning in two days.” And in this and other ways all the great navigators have been frustrated in their efforts, and have been more or less confounded in their attempts to sail round the Earth upon or beyond the antarctic circle. But if the southern region is a pole or centre, like the north, there would belittle difficulty in circumnavigating it, for the distance round would be comparatively small. When it is seen that the Earth is not a sphere, but a plane, having only one centre, the north; and that the south is the vast icy boundary of the world, the difficulties experienced by circumnavigators can be easily understood.

Having given a surface or bird’s-eye view of the Earth, the following sectional representation will aid in completing the description.

Section through earthFIG. 11.

FIG. 11.

E E represents the Earth; W W the “great deep,” or the waters which surround the land; N the northern centre; and S S sections of the southern ice. As the present description is purely zetetic, and as every fact must therefore have its fullest value assigned to it, and its consequences represented, a peculiarity must be pointed out in the foregoing diagram. It will be observed that from about the points E E the surface of the water rises towards the south S S. It is clearly ascertained that the altitude of the water in various parts of the world is much influenced by the pressure of the atmosphere—however thispressure is caused—and it is well known that the atmospheric pressure in the south is constantly less than it is in the north, and therefore the water in the southern region must always be considerably higher than it is in the northern. Hence the peculiarity referred to in the diagram. The following quotation from Sir James Ross’s voyages, p. 483, will corroborate the above statements:—“Our barometrical experiments appear to prove that a gradual diminution of atmospheric pressure occurs as we proceed southwards from the tropic of Capricorn. * * * It has hitherto been considered that the mean pressure of the atmosphere at the level of the sea was nearly the same in all parts of the world, as no material difference occurs between the equator and the highest northern latitudes. * * * The causes of the atmospheric pressure being sovery much lessin the southern than in the northern hemispheres remains to be determined.”

Thus, putting all theories aside, we have seen that direct experiment demonstrates the important truth,that the Earth is an extended Plane. Literally, “Stretched out upon the waters;” “Founded on the seas and established on the floods;” “Standing in the water and out of the water.” How far the southern icy region extends horizontally, or how deep the waters upon and in which the earth stands or issupported are questions which cannot yet be answered. In Zetetic philosophy the foundation must be well secured, progress must be made step by step, making good the ground as we proceed; and whenever a difficulty presents itself, or evidence fails to carry us farther, we must promptly and candidly acknowledge it, and prepare for future investigation; but never fill up the inquiry by theory and assumption. In the present instance there is no practical evidence as to the extent of the southern ice and the “great deep.” Who shall say whether the depth and extent of the “mighty waters”havea limit, or constitute the “World without end?”

Having advanced direct and special evidence that the surface of the earth is not convex, but, on the contrary, a vast and irregular plane, it now becomes important that the leading phenomena upon which the doctrine of rotundity has been founded should be carefully examined. First, it is contended that because the hull of an outward-bound vessel disappears before the mast head, the water is convex, and therefore the Earth is a globe. In this conclusion, however, there is an assumption involved, viz., that such a phenomenoncan onlyresult from a convex surface. Inquiry will show that this is erroneous. If we select for observation a few miles of straight and level railway, we shall find that the rails,which are parallel, appear in the distance to approach each other. But the two rails which are nearest together do so more rapidly than those which are farthest asunder, as shown in the following diagram,Figure 12.

Railway perspectiveFIG. 12.

FIG. 12.

Let the observer stand at the point A, looking in the direction of the arrows; and the rails 1.2.3.4. will appear to join at the point B, but the rail 5.6 will appear to have converged only as far as C towards B.

Again, let a train be watched from the point A inFigure 13.

Railway perspectiveFIG. 13.

FIG. 13.

The observer looking from A, with his eye midway between the bottom of the carriage and the rail, will see the diameter of the wheels gradually diminish as they recede. The lines 1.2 and 1.4 will appear to approach each other until at the point B they will come together, and the space,including the wheels, between the bottom of the carriage and the rail will there disappear. The floor of the carriage will seem to be sliding without wheels upon the rail 1.2; but the lines 5.6 and 7.8 will yet have converged only to C and D.

The same phenomenon may be observed with a long row of lamps, where the ground is a straight line throughout its entire length as represented inFigure 14.

Street lamps perspectiveFIG. 14.

FIG. 14.

The lines 1.2 and A D will converge at the point D and the pedestal of the lamp at D will seem to have disappeared, but the line 3.4, which represents the true altitude of the lamps, will only have converged to the point C.

A narrow bank running along the side of a straight portion of railway, upon which poles are placed for supporting the wires of the electric telegraph will produce the same appearance, as shown inFigure 15.

Railway perspectiveFIG. 15.

FIG. 15.

The bank having the altitude 1.3 and 2.4 will, in the distance of two or three miles (according to its depth) disappear to the eye of an observer placed at Figure 1; and the telegraph pole at Figure 2 will seem not to stand upon a bank at all, but upon the actual railway. The line 3.4 will merge into the line 1.2 at the point B, while the line 5.6 will only have descended to the position C.

Ship in perspectiveFIG. 16.

FIG. 16.

Many other familiar instances could be given to show the true law of perspective; which is, that parallel lines appear in the distance to converge to one and the same datum line, but to reach it at different distances if themselves dissimilarly distant. This law being remembered, it is easy to understand how the hull of an outward-bound ship, although sailing upon a plane surface disappears before the mast-head. InFigure 16, let A B represent the surface of the water; C H the line of sight; and E D the altitude of the mast-head. Then, as A B and C H are nearer to each other than A B and E D, they will converge and appear to meet at the pointH, which is the practical, or, as it would be better to call it, theopticalhorizon. The hull of the vessel being contained within the lines A B and C H, must gradually diminish as these converge, until at H, or the horizon, it enters the vanishing point and disappears; but the mast-head represented by the line E D is stillabovethe horizon at H, and will require to sail more or less, according to its altitude, beyond the point H before it sinks to the line C H, or, in other words, before the lines A B and E D form the same angle as A B and C H.

It will be evident also that should the elevation of the observer be greater than at C, the horizon or vanishing point would not be formed at H, but at a greater distance; and therefore the hull of the vessel would be longer visible. Or, if, when the hull has disappeared at H, the observer ascends from the elevation at C to a higher position nearer to E, it will again be seen. Thus all these phenomena which have so long been considered as proofs of the Earth’s rotundity are really optical sequences of the contrary doctrine. To argue that because the lower part of an outward-bound ship disappears before the highest the water must be round, is toassumethat aroundsurfaceonlycan produce this effect! But it is now shown that aplanesurfacenecessarilyproduces thiseffect; and therefore the assumption is not required, and the argument involved is fallacious!

It may here be observed that no help can be given to this doctrine of rotundity by quoting the prevailing theory of perspective. The law represented in the foregoing diagrams is the “law of nature.” It may be seen in every layer of a long wall, in every hedge and bank of the roadside, and indeed in every direction where lines and objects run parallel to each other; but no illustration of the contrary perspective is ever to be seen! except in the distorted pictures, otherwise cleverly and beautifully drawn as they are, which abound in our public and private collections.

The theory which affirms that parallel lines converge only to one and the same point upon the eye-line is an error. It is true only of lines equidistant from the eye-line. It is true that parallel lines converge to one and the sameeye-line, butmeet it at different distances when more or less apart from each other. This is the true law of perspective as shown by Nature herself; any other idea is fallacious and will deceive whoever may hold and apply it to practice.

As it is of great importance that the difference should be clearly understood, the followingdiagram is given. Let E L (Figure 17) represent the eye-line and C the vanishing point of the lines, 1 C 2 C; then the lines 3.4.5.6, although convergingsomewhereto the line E L, will not do so to the point C, but 3 and 4 will proceed to D and 5 and 6 to H. It is repeated, that linesequidistantfrom thedatumwill converge on thesame pointand at thesame distance; but linesnotequidistant will converge on the samedatumbut atdifferent distances! A very good illustration of the difference is given inFigure 18. Theoretic perspective would bring the lines 1, 2, and 3 to the samedatumline E L and to thesame pointA. But the trueor natural law would bring the lines 2 and 3 to the point A because equidistant from the eye-line E L; but the line 1 being farther from E L than either 2 or 3, would be taken beyond the point A on towards C, until it formed thesame angleupon the line E L as 2 and 3 form at the point A.

Vanishing pointsFIG. 17.

FIG. 17.

Vanishing pointsFIG. 18.

FIG. 18.

The subject of perspective will not be rendered sufficiently clear unless an explanation be given of the cause and character of what is technically called the “vanishing point.” Why do objects, even when raised above the earth, vanish at a given distance? It is known, and can easily be proved by experiment, that “the range of the eye, or diameter of the field of vision is 110°; consequently this is thelargestangle under which an object can be seen. The range of vision is from 110° to 1°. * * Thesmallestangle under which an object can be seen is upon an average for different sights the 60th part of a degree, orone minutein space; so that when an object is removed from the eye 3000 times its own diameter, it will only just be distinguishable; consequently, the greatest distance at which we can behold an object, like a shilling, of an inch in diameter is 3000 inches or 250 feet.”[3]It may, therefore, be very easily understood that a line passing over the hull of a ship, and continuingparallel to the surface of the water, must converge to the vanishing point at the distance of about 3000 times its own elevation; in other words, if the surface of the hull be 10 feet above the water it will vanish at 3,000 times 10 feet; or nearly six statute miles; but if the mast-head be 30 feet above the water, it will be visible for 90,000 feet or over 17 miles; so that it could be seen upon the horizon for a distance of eleven milesafter the hull had entered the vanishing point! Hence the phenomenon of a receding ship’s hull being the first to disappear, which has been so universally quoted and relied upon as proving the rotundity of the Earth is fairly and logically a proof of the very contrary! It has been misapplied in consequence of an erroneous view of the law of perspective, and the desire to support a theory. That it is valueless for such a purpose has already been shown; and that, even if there were no question of the Earth’s form involved, it could not arise from the convexity of the water, is proved by the following experiment:—Let an observer stand upon the sea-shore with the eye at an elevation of about six feet above the water, and watch a vessel until it is just “hull down.” If now a good telescope be applied the hull will be distinctlyrestored to sight! From which it must be concluded that it haddisappeared through the influence of perspective, and not from having sunk behind the summit of a convex surface! Had it done so it would follow that the telescope had either carried the line-of-sight through the mass of water, or over its surface and down the other side! But the power of “looking round a corner” or penetrating a dense and extensive medium has never yet been attributed to such an instrument! If the elevation of the observer be much greater than six feet the distance at which the vanishing point is formed will be so great that the telescope may not have power enough to magnify or enlarge the angle constituting it; when the experiment would appear to fail. But the failure would only be apparent, for a telescope of sufficient power to magnify at the horizon or vanishing point would certainly restore the hull at the greater distance.

[3]“Wonders of Science,” by Mayhew, p. 357.

Flat earth mapFIG. 19.

FIG. 19.

An illustration or proof of the Earth’s rotundity is also supposed to be found in the fact that navigators by sailing due east or west return in the opposite direction. Here, again, a supposition is involved, viz., that upon a globeonlycould this occur. But it is easy to prove that it could take place as perfectly upon a circular plane as upon a sphere. Let it first be clearly understood what is really meant by sailingdue east and west. Practically it issailing at right angles to north and south: this is determined ordinarily by the mariners’ compass, but more accurately by the meridian lines which converge to the northern centre of the Earth. Bearing this in mind, let N inFigure 19represent the northern centre; and the lines N. S. the directions north and south. Then let the small arrow, Figure 1, represent a vessel on the meridian of Greenwich, with its head W. at right angles, or due west; and the stern E due east. It is evident that inpassing to the position of the arrow, Figure 2, which is still due west or square to the meridian, the arc 1.2 must be described; and in sailing still farther under the same condition, the arcs 2.3, 3.4, and 4.1 will be successively passed over until the meridian of Greenwich, Figure 1, is arrived at, which was the point of departure. Thus a mariner, by keeping the head of his vessel due west, or at right angles to the north and south, practically circumnavigates a plane surface; or, in other words, he describes a circleupon a plane, at a greater or lesser distance from the centre N, and being at all times square to the radii north and south, he iscompelledto do so—becausethe earth is a plane, having a central region, towards which the compass and the meridian lines which guide him, converge. So far, then, from the fact of a vessel sailing due west coming home from the east, andvice versa, being a proof of the earth’s rotundity, it is simply a phenomenon, consistent with and dependent upon its being a plane! The subject may be perfectly illustrated by the following simple experiment:—Take a round table, fix a pin in the centre; to this attach a thread, and extend it to the edge. Call the centre the north and the circumference the south; then, at any distance between the centre and the circumference, a direction at right angles to the threadwill be due east and west; and a small object, as a pencil, placed across or square to the thread, to represent a ship, may be carried completely round the table without its right-angled position being altered; or, the right-angled position firmly maintained, the vessel must of necessity describe a circle on being moved from right to left or left to right. Referring again to the diagram,Figure 19, the vessel may sail from the north towards the south, upon the meridian Figure 1, and there turning due west, may pass Cape Horn, represented by D, and continue its westerly course until it passes the point C, or the Cape of Good Hope, and again reaches the meridian, Figure 1, upon which it may return to the north. Those, then, who hold that the earth is a globe because it can be circumnavigated, have an argument which is logically incomplete and fallacious. This will be seen at once by putting it in the syllogistic form:—

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